blind source unmixing in multi-spectral optoacoustic tomography

Blind source unmixing in multi-spectraloptoacoustictomography

Jurgen Glatz, Nikolaos C. Deliolanis,∗ Andr eas Buehler, DanielRazansky, and Vasilis Ntziachristos

Chair for Biological Imaging & Institute for Biological and Medical ImagingTechnische Universitat Munchen & Helmholtz Zentrum Munchen, Munich, Germany

∗[email protected]

Abstract: Multispectral optoacoustic (photoacoustic) tomography(MSOT) is a hybrid modality that can image through several millimetersto centimeters of diffuse tissues, attaining resolutions typical of ultrasoundimaging. The method can further identify tissue biomarkers by decom-posing the spectral contributions of different photo-absorbing moleculesof interest. In this work we investigate the performance of blind sourceunmixing methods and spectral fitting approaches in decomposing thecontributions of fluorescent dyes from the tissue background, based onMSOT measurements in mice. We find blind unmixing as a promisingmethod for accurate MSOT decomposition, suitable also for spectralunmixing in fluorescence imaging. We further demonstrate its capacity withtemporal unmixing on real-time MSOT data obtainedin-vivo for enhancingthe visualization of absorber agent flow in the mouse vascular system.

© 2011 Optical Society of America

OCIS codes:(170.5120) Photoacoustic Imaging; (170.6960) Tomography; (170.6280) Spec-troscopy, fluorescence and luminescence; (100.1455) Blind deconvolution.

References and links1. H. Zhang, K. Maslov, G. Stoica, and L. Wang, “Functional photoacoustic microscopy for high-resolution and

noninvasive in vivo imaging,” Nat. Biotechnol.24, 848–851 (2006).2. M. Xu and L. Wang, “Photoacoustic imaging in biomedicine,” Rev. Sci. Instrum.77, 041101 (2006).3. V. Ntziachristos, “Going deeper than microscopy: the optical imaging frontier in biology,” Nat. Methods7, 603–

614 (2010).4. C. G. A. Hoelen, F. F. M. de Mul, R. Pongers, and A. Dekker, “Three-dimensional photoacoustic imaging of

blood vessels in tissue,” Opt. Lett.23, 648–650 (1998).5. H. Fang, K. Maslov, and L. V. Wang, “Photoacoustic doppler effect from flowing small light-absorbing particles,”

Phys. Rev. Lett.99, 184501 (2007).6. P.-C. Li, S.-W. Huang, C.-W. Wei, Y.-C. Chiou, C.-D. Chen, and C.-R. C. Wang, “Photoacoustic flow measure-

ments by use of laser-induced shape transitions of gold nanorods,” Opt. Lett.30, 3341–3343 (2005).7. V. Ntziachristos and D. Razansky, “Molecular imaging by means of multispectral optoacoustic tomography

(MSOT),” Chem. Rev.110, 2783–2794 (2010).8. H.-P. Brecht, R. Su, M. Fronheiser, S. A. Ermilov, A. Conjusteau, and A. A. Oraevsky, “Whole-body three-

dimensional optoacoustic tomography system for small animals,” J. Biomed. Opt.14, 064007 (2009).9. J. Gamelin, A. Maurudis, A. Aguirre, F. Huang, P. Guo, L. V. Wang, and Q. Zhu, “A real-time photoacoustic

tomography system for small animals,” Opt. Express17, 10489–10498 (2009).10. A. Buehler, E. Herzog, D. Razansky, and V. Ntziachristos, “Video rate optoacoustic tomography of mouse kidney

perfusion,” Opt. Lett.35, 2475–2477 (2010).11. G. Busse and A. Rosencwaig, “Subsurface imaging with photoacoustics,” Appl. Phys. Lett.36, 815–816 (1980).12. A. Rosencwaig, “Potential clinical applications of photoacoustics,” Clin. Chem.28, 1878–1881 (1982).13. X. Wang, X. Xie, G. Ku, L. V. Wang, and G. Stoica, “Noninvasive imaging of hemoglobin concentration and oxy-

genation in the rat brain using high-resolution photoacoustic tomography,” J. Biomed. Opt.11, 024015 (2006).

#137541 - $15.00 USD Received 2 Nov 2010; revised 25 Jan 2011; accepted 30 Jan 2011; published 3 Feb 2011(C) 2011 OSA 14 February 2011 / Vol. 19, No. 4 / OPTICS EXPRESS 3175

14. D. Razansky, C. Vinegoni, and V. Ntziachristos, “Multispectral photoacoustic imaging of fluorochromes in smallanimals,” Opt. Lett.32, 2891–2893 (2007).

15. D. Razansky, M. Distel, C. Vinegoni, R. Ma, M. Perrimon, R. W. Koster, and V. Ntziachristos, “Multispectralopto-acoustic tomography of deep-seated fluorescent proteins in vivo,” Nat. Photonics3, 412–417 (2009).

16. P.-C. Li, C.-R. C. Wang, D.-B. Shieh, C.-W. Wei, C.-K. Liao, C. Poe, S. Jhan, A.-A. Ding, and Y.-N. Wu, “Invivo photoacoustic molecular imaging withsimultaneous multiple selective targeting using antibody-conjugatedgold nanorods,” Opt. Express16, 18605–18615 (2008).

17. A. Taruttis, E. Herzog, D. Razansky, and V. Ntziachristos, “Real-time imaging of cardiovascular dynamics andcirculating gold nanorods with multispectral optoacoustic tomography,” Opt. Express18, 19592–19602 (2010).

18. D. Razansky, J. Baeten, and V. Ntziachristos, “Sensitivity of molecular target detection by multispectral optoa-coustic tomography (MSOT),” Med. Phys.36, 939–945 (2009).

19. A. Rosenthal, D. Razansky, and V. Ntziachristos, “Quantitative optoacoustic signal extraction using sparse signalrepresentation,” IEEE Trans. Med. Imaging28, 1997–2006 (2009).

20. I. T. Jolliffe,Principal Component Analysis, 2nd ed. (Springer, 2002).21. A. Cichocki, R. Zdunek, A. H. Phan, and S. I. Amari,Nonnegative Matrix and Tensor Factorizations: Applica-

tions to Exploratory Multi-way Data Analysis and Blind Source Separation, 1st ed. (Wiley, 2009).22. R. Tauler, B. Kowalski, and S. Fleming, “Multivariate curve resolution applied to spectral data from multiple

runs of an industrial process,” Anal. Chem.65, 2040–2047 (1993).23. A. Hyvarinen, J. Karhunen, and E. Oja,Independent Component Analysis, Adaptive and Learning Systems for

Signal Processing, Communications, and Control, 1st ed. (Wiley InterScience, 2002).24. M. Funaro, E. Oja, and H. Valpola, “Independent component analysis for artefact separation in astrophysical

images,” Neural Networks16, 469–478 (2003).25. B. A. Draper, K. Baek, M. S. Bartlett, and J. R. Beveridge, “Recognizing faces with pca and ica,” Comput. Vis.

Image Underst.91, 115 – 137 (2003).26. J. Yang, D. Zhang, A. F. Frangi, and J. Y. Yang, “Two-dimensional pca: a new approach to appearance-based

face representation and recognition,” IEEE Trans. Pattern Anal. Mach. Intell.26, 131–137 (2004).27. E. M. C. Hillman and A. Moore, “All optical anatomical co registration for molecular imaging of small animals

using dynamic contrast,” Nat. Photonics1(9) 526–530 (2007).28. H. Xu and B. W. Rice, “In-vivo fluorescence imaging with a multivariate curve resolution spectral unmixing

technique,” J. Biomed. Opt.14, 064011 (2009).29. A.-S. Montcuquet, L. Herve, F. Navarro, J.-M. Dinten, and J. I. Mars, “Nonnegative matrix factorization: a blind

spectra separation method for in vivo fluorescent optical imaging,” J. Biomed. Opt.15, 056009 (2010).30. S. Clemencon and S. Slim, “On portfolio selection under extreme risk measure: the heavy-tailed ICA Model,”

Int. J. Theor. Appl. Finance10, 449–474 (2007).31. N. Keshava, “A survey of spectral unmixing algorithms,” Lincoln Lab. J.14, 55–78 (2003).32. E. Moore, “On the reciprocal of the general algebraic matrix,” Bull. Am. Math. Soc.26, 394–395 (1920).33. R. Penrose, “A generalized inverse for matrices,” in Proceedings of the Cambridge Philosophical Society, (1955),

Vol. 51, pp. 406–412.34. K. Pearson, “On lines and planes of closest fit to a system of points in space,” London, Edinburgh Dublin Philos.

Mag. J. Sci.6, 559–572 (1901).35. S. M. Kay,Fundamentals of Statistical Signal Processing, 1st ed. (Prentice Hall PTR, 1993),Vol. 1.36. J. Nash, “The singular-value decomposition and its use to solve least-squares problems,” inCompact Numerical

Methods for Computers: Linear Algebra and Function Minimization, 2nd ed. (Inst. of Physics Pub., 1990), pp.30–48.

37. L. Le Cam, “The central limit theorem around 1935,” Stat. Sci.1, 78–91 (1986).38. A. Hyvrinen, “Fast and robust fixed-point algorithms for independent component analysis,” IEEE Trans. Neural

Netw.10, 626–634 (1999).39. M. Xu and L. V. Wang, “Universal back-projection algorithm for photoacoustic computed tomography,” Phys.

Rev. E71, 016706 (2005).

1. Introduction

Optoacoustic(or photoacoustic) imaging is a potent imaging method that can offer high resolu-tion visualization of optical absorption deep in living tissues [1, 2, 3]. Being a hybrid technique,it combines the advantages of visualizing highly specific optical absorption contrast with thehigh spatial resolution of ultrasound. Recording optoacoustic signals emitted by tissues frommultiple projections, in response to the absorption of ultrafast light pulses by tissue elements,allows obtaining tomographic reconstructions of light absorbing structures in deep tissues atresolutions of tens of micrometers and below. The potential of this technology has been demon-strated in many applications, in particular imaging of blood vessels [4], blood flow [5, 6] or


using various photo-absorbing agents and nanoparticles [7]. Recently, the use of acoustic de-tectorarrays has eliminated the need for mechanical scanning of a single detector and enabledvideo rate optoacoustic imaging [8, 9, 10], allowing a wide number of possible applicationsin both clinical research and drug discovery. While subsurface imaging at the microscopic ormacroscopic regimes has been suggested since the early 80’s [11, 12], optoacoustic imaginghas significantly improved in recent years. Of particular importance are spectral imaging meth-ods where tissues are excited at two or more wavelengths and generate in response images ofthe bio-distribution of various tissue molecules or biomarkers, for example in visualizing oxy-gen saturation [13], extrinsically administered fluorochromes [14], fluorescent proteins [15] orcirculating nanoparticles [16, 17].

In many cases, the contributions of various photo-absorbing agents, such as contrast agents,targeted probes or nanoparticles may constitute only small signal variances over the backgroundabsorption, depending on their concentration. This may complicate the detection of the pho-toabsorbing agent on single wavelength images, even if the selected wavelength correspondsto the absorption maximum of the agent of interest. When data at multiple wavelengths areobtained however, it is possible to improve the contrast and detection sensitivity by resolvingthe spectral signature of the absorber agent used over other non-specific spectral contributions,e. g. from highly absorbing hemoglobin.

Unmixing methods based on differential or fitting algorithms use the known spectral or tem-poral information to process the image on a pixel-by-pixel basis. This separation can be chal-lenging since the exact spectral profile of the background contribution is not always known inin-vivo tissue imaging. In addition, the spectral signature of the agent of interest may also benot accurately known, for instance the absorption spectrum may change in different biochem-ical environments. Moreover, light attenuation and ultrasonic dispersion in tissues leads to acorresponding non-linear relationship between the measured optoacoustic signals and the cor-responding target concentration, as a function of depth, or target size [18]. This is particularlyevident for volumetric tissue imaging since the optoacoustic signals depend on the product ofthe local light fluence at different depths times the local absorption coefficient of the agent ofinterest and other background chromophores [19]. Finally, the spectral profile of light propagat-ing in tissue is also altered by depth, since different wavelengths are attenuated by a differentrate, which may also contribute to intensity variations in the recorded MSOT signals with depth.

These potential complications in spectral unmixing may be addressed with the use of mul-tivariate data analysis and matrix factorization algorithms, such as principal component analy-sis (PCA) [20], non-negative matrix factorization (NNMF) [21], multivariate curve resolution(MCR) [22], or independent component analysis (ICA) [23]. Applications of these methodsinclude astronomy [24], pattern recognition [25, 26], anatomical segmentation [27], fluores-cence imaging [28, 29], and finance [30]. Herein we have investigated PCA and ICA in spectralunmixing of optoacoustic images and compared them with spectral fitting schemes. Contraryto the pixel-by-pixel processing approach in the differential and fitting unmixing methods, thekey element in the multivariate approaches is the unaided identification of changes that is com-mon across various pixels, helping to identify contrast agents that have a non-uniform spatialbio-distribution. Of particular interest in the context of unmixing MSOT measurements wasthe behavior of these algorithms concerning the dependence of the optoacoustic signals ondepth and other tissue optical parameters, as well as biologically relevant spectral shifts of thedetected fields. We have examined the performance of the unmixing methods in spectral andtemporal decomposition of tissue components inin-vivoandex-vivoexperiments.


2. Theory

Generally, the term ”unmixing” refers to the unsupervised decomposition of mixed observationsinto usually a smaller number of endmembers [31]. Its purpose is to improve the spectral ortemporal resolution by identifying a small number of underlying sources that are superposedto yield the measured data and to separate them into individual images. For simplicity, in thefollowing description we use the terminology of the spectral domain, but the methodology holdsfor the temporal domain as well.

2.1. Spectral Fitting

The most commonly employed unmixing method is spectral fitting, i. e. finding the sourcecomponent that best fits a given absorption spectrum in the least-squares sense. Given the(n×m) multispectral measurement matrixM, where n is the number of image pixels andm isthe number of measurements, as well as the(k×m) spectral matrixS with the absorptioncoefficients of thek components at them measurement wavelengths, the data can be unmixedwith the Moore-Penrose pseudoinverse [32, 33]S+.

S+ = ST (

SST)−1. (1)

With this generalized inverse, the source component reconstructionRpinv, which best fits thespectra inScan be determined as

Rpinv = MS+. (2)

The performance of the spectral fitting method depends on the accuracy and completeness ofthe absorption spectra and the absence of systematic errors in the data. It therefore becomeschallenging to apply the method when reliable spectral information for all potential contribu-tions in the signal is not available, for instance forin-vivo tissue measurements. In such cases,approaches that do not requirea priori spectral information may be beneficial.

2.2. Principal Component Analysis

Principal Component Analysis [34, 35] is a blind source unmixing technique, that is based onthe assumption that the source components are statistically uncorrelated. PCA yields a linearorthogonal transformation into a new coordinate system, in which the largest data variance isprojected onto the first principal component, the largest remaining variance onto the second one,and so on. Consequently, the correlated measurement data is unmixed by being transformed touncorrelated principal components. PCA can be calculated as a singular value decomposition[36] of M or as an eigenvalue decomposition of its covariance matrix [20]. In both cases, notonly the unmixed componentsRPCA but also the corresponding transformation matrixUPCA

are returned by the PCA algorithm, i. e.

RPCA = UTPCAM. (3)

Since the eigenvector matrixUT is orthonormal, its inverse isU. The matrixU represents theabsorption spectra of the calculated principal components, as multiplying the principal com-ponent vectors by it would merge them again into the measured data. This spectral estimationcan be used to identify the correspondence between a principal component and a specific ab-sorber of interest. Furthermore, the corresponding eigenvalues are also computed; their relativevalue indicates the data variance represented in the component. This can be used for dimen-sion reduction when the number of multispectral measurements exceeds the number of sourcecomponents and to discard principal components that contain mostly noise or artifacts.


2.3. Independent Component Analysis

IndependentComponent Analysis [23] (ICA) is yet another blind source separation technique,but it is based on a different assumption about the sources than PCA. While the latter as-sumes uncorrelated sources, ICA finds endmembers that satisfy the more general and thereforestronger condition of statistical independence. The algorithm seeks a transformation of thedependent mixed spectral components into a set of independent source components and alsoyields the corresponding mixing matrixUICA , i. e.

RICA = UTICAM. (4)

According to the central limit theorem [37], a sum of non-gaussian variables is closer to a gaus-sian distribution than the original variables. Consequently, the mixed multispectral measure-ments are expected to be more gaussian than the unmixed independent components. Herein,we employ the FastICA algorithm [38], which finds the independent sources by using a fixedpoint iteration scheme in order to maximize non-Gaussianity, as measured by kurtosis, a fourthorder statistical moment. By maximizing the kurtosis of the components, a non-Gaussian, andthus an independent representation is found. A key difference between ICA and PCA is that noeigenvalues and hence no measure of a component’s significance is obtained.

As a consequence, ICA requires some preprocessing when dealing with large datasets be-cause it attempts to retrieve as many components as the number of available measurements andcannot sort out superfluous signals on its own. Thus, many independent components merelyrepresent noise or minor signal variations, which makes the interpretation of the results moredifficult. A logical solution would be using PCA as a preprocessing step. Thereby, the data areinitially analyzed by PCA and the insignificant principal components, mainly containing noise,can be discarded. This step not only serves to eliminate the noise but also reduces the dimensionof the data, presenting the ICA algorithm with a better conditioned problem. WhenR′

PCA isthe reduced PCA subset, the unmixing is denoted by

RPCA/ICA = UTICAR′

PCA = UTICAU′T

PCAM. (5)

Equation (5) also shows that the estimated spectral characteristics of the unmixed componentscan be retrieved as the product of the two mixing matricesUT

ICA andU′TPCA.

3. Experimental Methods

3.1. Experimental system and data processing

Experimental MSOT measurements were performed with a real-time MSOT scanner, previ-ously described in Ref. [10]. Briefly, a tunable (680 – 950 nm) pulsed (<10 ns) optical para-metric oscillator laser (Opotek Inc., Carlsbad, CA, USA) with a 10 Hz repetition rate is used forsignal generation. The laser beam is guided into a silica fused-end fiber bundle (CeramOptecGmbH, Bonn, Germany) creating a ring shaped illumination pattern of∼7 mm width upon thesurface of the animal. Signal collection is based on a custom-made 64-element focused trans-ducer array (Imasonic SaS, Voray, France) covering a solid angle of 172◦ around the imagedobject, while the detection plane coincided with the center of the illumination ring. The indi-vidual detection elements are manufactured using piezocomposite technology with a centralfrequency of 5 MHz, a bandwidth (−6 dB) of more than 50% sensitivity of∼ 18µV/Pa andare shaped to create a cylindrical focus at 40 mm. The detected signals are digitized at a sam-pling frequency of 60 MHz by 8 multi-channel analog to digital converters (Model PXI5105,National Instruments, Austin, TX, USA) with noise floor of∼ 3.8 nV/

√Hz. A linear stage

(NRT150, Thorlabs GmbH, Karlsfeld, Germany) allows linear translation of the animal holder


in the axialz direction.The data acquisition is synchronized so that the signals are acquiredonly when the stage comes to a complete rest. For all experiments the optoacoustic pressuredistribution was reconstructed with a filtered backprojection algorithm [39].

3.2. Animal preparation and imaging

For spectral unmixing, a nude mouse cadaver phantom with two inclusions of fluorophores sim-ulating tumors was prepared. The inclusions consisted of 1% agar solution and 1% intralipid(Sigma-Aldrich, St. Louis, MO, USA), which was initially heated to 90◦C. While cooling downto 50◦C, solutions of 12.9 µM of ICG (peak absorption≈ 800 nm, Pulsion Medical, Munich,Germany) and 3.7µM of Cy7 Cyanine Dye (peak absorption≈ 750 nm, GE Healthcare, LittleChalfont, UK) were prepared to both have 2 cm−1 optical density at their absorption peaks. At35 ◦C, 50µL of each solution was injected subcutaneously in the upper back / neck area of aeuthanized mouse and were left to equilibrate with room temperature and solidify to a shapethat is similar to a subcutaneous tumor.The mouse was positioned in supine position inside a water-impenetrable yet transparent mem-brane, providing a wide tomographic view of∼ 180◦. A total of 31 spectral measurements inthe 700 – 850 nm range were acquired in steps of 5 nm and reconstructed with the filteredbackprojection algorithm [39]. Interwavelength variations have been normalized by powerme-ter readings (Model FieldMaxII-TOP, Coherent GmbH, Dieburg, Germany) for quantitativemultispectral reconstructions.

For imaging and unmixing in the time domain, a white CD1 mouse was anesthetized withketamine and xylazine mixture, catheterized in the right tail vein and injected with 50µL ofblack india ink saline solution as contrast medium. An axial slice in the pelvic region, approxi-mately 2 cm away from the catheter towards the heart, was imaged with MSOT for 80 s, usingherein data at 1 Hz frame rate, after performing 10 signal averages at a wavelength of 800 nm.After imaging, the mouse was euthanizedin situ.

4. Spectral domain unmixing

We showcase the described methods on the reconstructions from the absorber implantation ex-periment, where the presence of two contrast agents with an overlapping spectrum presents achallenging unmixing problem. Reconstructions of an axial slice in the neck area at 4 represen-tative wavelengths are shown in Fig. 1

ICG Cy7

700 nm 750 nm 800 nm 850 nm

Fig. 1. Optoacoustic reconstruction of an axial slice at the neck area at 4 representativeexcitation wavelengths. The green and the cyan highlighted areas in the first image indicatethe locations of the ICG and Cy7 implantations.

The two implantations can be easily identified in the left and the right side of the mouse neckunder the skin. It can be observed that the reconstructed optoacoustic signal at the Cy7 implan-tation area has a peak at about 750 nm while at the ICG area the peak is at around 800 nm, whichcorrelates well with the expected absorption peaks of the corresponding dyes. The ICG, Cy7


and background components, unmixed by fitting (pseudoinverse), PCA, and ICA are displayedin Fig. 2. The spectral absorption data of the two fluorochromes and deoxygenated hemoglobin,that were used for the fitting unmixing method, as well as the corresponding spectra calculatedby ICA, are shown in Fig. 3. Deoxygenated hemoglobin was chosen as the background absorbersince it is assumed to be the dominant absorber in the dead tissue.

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ba

ckg

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nd

ICG

Cy7

PCA ICA

Fig. 2. Comparison of the performance of the unmixing methods, showing the respectivesourcecomponents calculated for the ICG and Cy7 inclusions and the tissue backgroundwith the three unmixing methods.

The images show that all three methods successfully managed to isolate the two fluorochromecomponents from the background. However, fitting with the pseudoinverse algorithm yieldedcrosstalk of the background signal into the ICG and Cy7 components. Unmixing with PCAalso exhibited crosstalk, which is attributed to the orthogonality criterion that is imposed. Onthe other hand, ICA accurately unmixed the components and the spectra calculated are veryclose to the expected spectra of the employed fluorochromes. The correspondence betweenthe ICA spectra and the known absorption curves was determined by visual inspection andthe ICA components were allocated accordingly. Using Pearson’s product moment correlationcoefficientρ , the correlation between the known spectra and the ones estimated by ICA wascalculated to beρ = 0.91 for the background,ρ = 0.83 for ICG andρ = 0.96 for Cy7. In orderto evaluate the performance of the unmixing methods the signal-to-background ratios (SBR)were calculated using the standard deviation of the pixel values for the two fluorochrome in-clusions. The results, as shown in Table 1 coincide with the visual examination that the ICAunmixing method outperforms fitting and PCA.

The proposed preprocessing of ICA by PCA was also applied to this dataset. While it reducedthe number of components and, thus, made the identification and allocation of the componentseasier, the unmixed images did not improve upon ICA alone, since the two results were virtuallyindistinguishable.

The results demonstrate the usefulness of blind source unmixing methods in the analysis of


600 650 700 750 800 850

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Fig. 3. Absorption spectra of ICG and Cy7 (solid lines) and the corresponding spectraestimatedby the ICA analysis (lines with markers). Dashed lines are fitting curves for theICA spectra.

Table 1.Signal-to-Background Ratio (SBR) of the Two Inclusion Areas for the Differ-ent Unmixing Methods

Unmixing method ICG inclusion Cy7 inclusionfitting 2.9 7.8PCA 1.8 3.4ICA 6.7 10.4

MSOT measurements. In particular, ICA appears more suited for MSOT imaging as it yieldsbetterseparation of components than PCA or spectral fitting methods, exhibiting a significantlyhigher SBR for both ICG and Cy7.

5. Time domain unmixing

The imaging of circulation dynamics by MSOT in combination with time domain unmixing isdemonstrated on the experimental data shown in Fig. 4. In the field of view, various anatomicalstructures can be seen, such as the bladder, spine, and the extensions of the right and the lefttail veins in the torso (Fig. 4a). The right tail vein appears to be less absorbing because of thelower blood volume due to the restriction of flow from catheterization.

Images acquired at different time points are shown in Figs. 4b-d. ICG was injected att =10 s leading to a notably increasing and then gradually decreasing signal in the right vein.A few seconds later the signal in the left vein showed an oscillatory pattern that eventuallyfaded out, indicating that the absorber was fully diluted in the blood stream after 50 s. Toinvestigate the unmixing methods in the time domain, we examined the ability to separatethe tissue components based on the dynamic changes of the images. The first three principlecomponents from PCA on the full 80-frame time-series and the corresponding temporal profiles(eigenvectors) are shown in Figs. 5a-d.

The first principal component contains mainly the parts of the image that remain constant, the


b: t = 11 s c: t = 17 s d: t = 25 s a: anatomical

i.

m.

Fig. 4. Temporal optoacoustic images of the pelvic region (axial slices). a) high contrast (toenhancethe anatomical features) b-d) reconstruction in three representative time points. i.:injection vein, m.: monitor vein.

e: injection vein f: monitor vein g: overlay f.

a: PC 1 b: PC 2 c: PC 3 d:

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Fig. 5. Temporal unmixing of tissue components. a-c) the first three principal componentsof PCA. d) the temporal profiles associated with these components. e-g) the two vein com-ponents after the combined PCA-ICA analysis and their overlay onto the anatomical image.h) the temporal profiles of the injection in the monitor vein.

second one shows the most prominent changes in the images, whereas the third one shows thechanges with respect to the two previous ones and so forth. Due to the orthogonality criterion,the PCA components do not disentangle the two types of veins and the temporal profiles alsoshow negative values that make it difficult to identify a specific temporal pattern. Principalcomponents from 8 to 80 mostly contain noise. On the other hand, performing ICA directly onthe full set of 80 images yielded a large number of independent components (not shown), whichwere not found useful as they represented minor changes in the images, such as variationsintroduced by laser power fluctuations, mouse movement and noise. A third combinationalmethod proved to be most viable, where PCA was employed as a preprocessing step for ICA.As stated above, the first eight PCA components practically contain all the useful informationon the temporal variations. This reduced subset can subsequently be used as an input into ICA,feeding the algorithm with a better-conditioned dataset. After noise reduction achieved by PCApre-processing, ICA yielded the components shown in Figs. 5e-g. The temporal profiles can becomputed as a product of the PCA and ICA mixing matrices and are shown in Fig. 5f.


6. Discussion and Conclusion

With the emergence of real-time MSOT [10, 17], spectral decomposition of various tissuebiomarkers and dynamic monitoring of internal or external photo-absorbing molecules has be-come possible in small animals. The post-processing of the generated spectral and temporaldata requires however a robust and reliable method for decomposing the constitutive contribu-tions from the measurements. In this paper, we have suggested and experimentally examinedthe blind source unmixing approach as a very promising alternative to separating mixed com-ponent data by fitting. Fitting requires the knowledge of the spectral or temporal profiles ofall components to compute a generalized inverse of the mixing matrix. However, these are of-ten not available for all sources with the necessary accuracy. The primary advantage of blindunmixing is that noa priori information is needed, making the technique suitable for a widerange of applications. It can separate contrast agents of a common spectral or temporal bio-distribution from background absorbers such as hemoglobin. The unmixing quality of PCAand ICA demonstrated herein on mouse measurements was found to be superior to spectralfitting, further generating components that can lead to spectral identification of specific tissuebiomarkers such as hemoglobin or the contributions of intrinsically expressed or administeredmolecular probes. Additionally, the use of blind unmixing was successfully demonstrated inthe time domain by separation of blood veins based on dynamic changes of an optoacousticimage sequence. It is evident, that the sensitivity of the imaging systems directly benefits froman improved unmixing performance.

Among the discussed blind source methods ICA appears to be the superior method, yieldinga cleaner unmixing compared to PCA in the spectral domain. Contrary to spectral unmixing,it is unlikely to have ana priori knowledge of temporal profiles of biological processes or thecontrast agent’s temporal biodistribution in living organisms. Therefore fitting procedures arenot common in dynamic measurements. In response, we found that temporal unmixing basedon blind decomposition methods required a combination of PCA and ICA to lead to clearlyperceived time components.

Future research will aim to further evaluate the performance of blind source techniques inthe unmixing of MSOT data and to define suitable pre- and post-processing steps that canhelp to automate the procedure and also guide the unmixing witha priori information thatmay be available. Applications of these unmixing methods are envisioned also in the fieldof optical fluorescence imaging, where they can help to increase detection sensitivity, and inautofluorescence removal.

Acknowledgements

The authors would like to thank Dr. George Themelis for the helpful discussions, and Dr. NielsHarlaar for the help in the surgical procedures. N. C. D. is supported by a Marie Curie Intra-European Fellowship within the 7th European Community Framework. D. R. acknowledgessupport from the German Research Foundation (DFG) Research Grant (RA 1848/1). V. N. ac-knowledges support from an ERC Advanced Investigator Award and BMBF’s Medizintechnikaward.


blind source unmixing in multi-spectral optoacoustic tomography

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